The Problem of Three Stars: Stability Limit

Valtonen, M. J.; Mylläri, Aleksandr; Орлов, В. В.; Rubinov, A.

doi:10.1017/s1743921308015627

Cited by 16 publications

(12 citation statements)

References 11 publications

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“…The three-body problem is an old topic in celestial mechanics, with wide astrophysical applications in the Solar system and beyond (Valtonen et al 2008;Innanen et al 1997;Holman et al 1997). Hierarchical triple systems are systems in which an inner binary orbits a more distant object on an outer orbit, with some mutual given inclination between the inner and outer orbits.…”

Section: Introductionmentioning

confidence: 99%

“…The general equations of motion of the three-body problem cannot be solved analytically (Valtonen & Karttunen 2006), however secular averaging analysis can be used to describe a wide range of cases. For hierarchical systems, pioneering works of Lidov (1962) and Kozai (1962) have shown that the torque of the outer binary can induce significant quasi-periodic oscillations in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

Grishin¹,

Perets²,

Zenati³

et al. 2016

Mon. Not. R. Astron. Soc.

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A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasistable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (∼ 120• ), beyond which the agreement is marginal. At such high inclinations the stability radius is larger, the ratio between the outer and inner periods becomes comparable, and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non co-planar systems, our results have direct implications for any triple systems, and in particular binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

Grishin¹,

Perets²,

Zenati³

et al. 2016

Mon. Not. R. Astron. Soc.

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“…Predictions of two stability criteria were tested against the numerical results for the fraction of escaping stars shown in Figure 1. These being the MSC discussed in the previous section and the stability criterion from Valtonen et al (2008) which Zhuchkov et al (2010) found to be the most accurate stability criterion of those they tested. Orbital inclination effects are included in the Valtonen et al (2008) stability criterion, however there is no treatment of the eccentricity of the inner orbit (ei).…”

Section: Testing Stability Of Inclined Systemsmentioning

confidence: 99%

“…The stability criterion used in Aarseth (2003) does not include any inclination dependence and is not accurate for the high mass ratios in the galaxy-GC system. Therefore in Section 3 we compare the Mardling stability predictions and the stability criterion of Valtonen et al (2008) to numerical experiments of inclined orbits.…”

Section: Introductionmentioning

confidence: 99%

Application of three-body stability to globular clusters – I. The stability radius

Kennedy

2014

Monthly Notices of the Royal Astronomical Society

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The tidal radius is commonly determined analytically by equating the tidal field of the galaxy to the gravitational potential of the cluster. Stars crossing this radius can move from orbiting the cluster centre to independently orbiting the galaxy. In this paper the stability radius of a globular cluster is estimated using a novel approach from the theoretical standpoint of the general three-body problem. This is achieved by an analytical formula for the transition radius between stable and unstable orbits in a globular cluster.A stability analysis, outlined by Mardling (2008), is used here to predict the occurrence of unstable stellar orbits in the outermost region of a globular cluster in a distant orbit around a galaxy. It is found that the eccentricity of the cluster-galaxy orbit has a far more significant effect on the stability radius of globular clusters than previous theoretical results of the tidal radius have found. A simple analytical formula is given for determining the transition between stable and unstable orbits, which is analogous to the tidal radius for a globular cluster. The stability radius estimate is interior to tidal radius estimates and gives the innermost region from which stars can random walk to their eventual escape from the cluster. The timescale for this random walk process is also estimated using numerical three-body scattering experiments.

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“…The authors obtained the family of orbits, and according the criterion χ 2 , the orbital period of the best solution is equal to 4000 years. The decay probability of this triple system was calculated by numerical simulations (see , by the criteria of Aarseth (Aarseth 2003) and of Valtonen et al (Valtonen 2008). For e=0.1 the decay probability is less than 2%; for e=0.39 maximal values of the decay probabilities are following: 15% (simulations), 26% (Aarseth), 29% (Valtonen).…”

Section: T Tauri=wds 04220+1932=hip 20390mentioning

confidence: 99%

Dynamical investigations of the multiple stars

Kiyaeva

Zhuchkov

2017

Open Astronomy

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Two multiple stars -the quadruple star κ Bootis (ADS 9173) and the triple star T Taury were investigated. The visual double star κ Bootis was studied on the basis of the Pulkovo 26-inch refractor observations 1982-2013. An invisible satellite of the component A was discovered due to long-term uniform series of observations. Its orbital period is 20 ± 2 years. The known invisible satellite of the component B with near 5 years period was confirmed due to high precision CCD observations. The astrometric orbits of the both components were calculated. The orbits of inner and outer pairs of the pre-main sequence binary T Taury were calculated on the basis of high precision observations by the VLT and on the Keck II Telescope. This weakly hierarchical triple system is stable with probability more than 70%.

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The Problem of Three Stars: Stability Limit

Cited by 16 publications

References 11 publications

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

Application of three-body stability to globular clusters – I. The stability radius

Dynamical investigations of the multiple stars

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